President Barack Obama, accompanied by House Speaker John Boehner of Ohio, speak to reporters in the Roosevelt Room of the White House in Washington on Nov. 16 as he hosts a meeting of the bipartisan, bicameral leadership of Congress to discuss the deficit and economy in Washington.The Associated Press

WASHINGTON — President Barack Obama and leaders of the lame-duck Congress may be just weeks away from shaking hands on a deal to avert the dreaded “fiscal cliff.” So it’s natural to wonder: If they announce a bipartisan package promising to curb mushrooming federal deficits, will it be real?

Both sides have struck cooperative tones since Obama’s re-election. Even so, he and House Speaker John Boehner (R-Ohio) the GOP’s pivotal bargainer, have spent most of the past two years in an acrid political climate in which both sides have fought stubbornly to protect their constituencies.

Obama and top lawmakers could produce an agreement that takes a serious bite out of the government’s growing $16 trillion pile of debt and puts it on a true downward trajectory.

Or they might reach an accord heading off massive tax increases and spending cuts that begin to bite in January — that’s the fiscal cliff — while appearing to be getting tough on deficits through painful savings deferred until years from now, when their successors might revoke or dilute them.

The House and Senate have four weeks until Christmas. Their leaders and the president want a deal before then. Bargainers are shooting for a framework setting future debt-reduction targets, with detailed tax and spending changes to be approved next year but possibly some initial savings enacted immediately.

Obama has suggested 10-year savings totaling around $4.4 trillion.

Passing a framework next month that sets deficit-cutting targets for each of the next 10 years would be seen as a sign of seriousness. But look for specifics.

An agreement will have a greater chance of actually reducing deficits if it details how the savings would be divided between revenue increases and cuts in federal programs, averting future fights among lawmakers over that question.

Better yet would be including a fast-track process for passing next year’s tax and spending bills if they meet the savings targets so they can whisk through Congress without the possibility of a Senate filibuster, in which 41 of the 100 senators could kill a measure they dislike.

Another sign of sincerity: An enforcement mechanism that imposes savings automatically if lawmakers gridlock over details. Legislators’ efforts now to avert January’s combination of automatic tax boosts and spending cuts underscores the effectiveness of forcing them to act.

Less impressive would be verbal pledges by the White House and congressional leaders to meet deficit-cutting goals without passing legislation inscribing the figures into law.

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